Question

If: $2^{x+y}=6^y$ ,$3^x=3\cdot 2^{y+1}$. Find $x\log 2-y\log 3$

Answer 1

$2^{x+y}=6^y$

$\Rightarrow 2^x\times 2^y=2^y\times 3^y$

$\Rightarrow 2^x=3^y$

$\Rightarrow x\log 2=y\log 3$

$\Rightarrow x\log 2-y\log 3=0$